AbstractâThe Hemispherical Resonator Gyro (HRG) has proven itself to be an ultra ... rate. Illustrated in Fig. 1 are the two orthogonal gyro axes oriented at some ...
ISSN 20751087, Gyroscopy and Navigation, 2012, Vol. 3, No. 4, pp. 227–234. © Pleiades Publishing, Ltd., 2012.
MilliHRG Inertial Navigation System D. Meyer and D. Rozelle Northrop Grumman – Navigation Systems Division, Woodland Hills, CA, USA Received May 10, 2012
Abstract—The Hemispherical Resonator Gyro (HRG) has proven itself to be an ultrareliable technology for space application with over 18 million operation hours and 100% mission success. Northrop Grumman Nav igation Systems Division is developing a terrestrial inertial navigation system (INS) based on the proven space technology that can be used for precision pointing applications. The Precision Pointing System (PPS) design yields a small size and lightweight system and will require only a few watts of power to operate. To achieve this small sized INS, the PPS utilizes a new golfball sized milliHRG (mHRG) that is based on the current HRG 130P production gyro design used in extremely accurate space pointing systems. The power reduction is derived from a new electronics design based around low power elements. The new mHRG gyro design has demonstrated bias stability performance better than the navigation grade gyros and will quickly attain this accuracy due to the extremely low noise characteristics of the HRG. Instrumental in the success of the mHRG performance has been the implementation of a calibration mechanization that eliminates the requirement for thermal control or modeling. This implementation will allow the INS to align quickly and will be advantageous for applications that have a quick response time requirement. Additionally, due to the stability of the mHRG the system can operate without GPS aiding for greater than an hour, while maintaining the attitude accuracy required for precision pointing, before an internal realignment is needed. The simpli fied design of mHRG has reduced the parts count by roughly 90% when compared to the current space qual ified HRG production unit. With the major parts reduction it is projected that the mHRG can be produced efficiently and at a cost making it a viable choice for terrestrial applications. DOI: 10.1134/S2075108712040086
INTRODUCTION The Hemispherical Resonator Gyro, HRG, has it’s notional roots back in the late 19th century when G.H. Bryan had his seminal paper, ‘On the beats in the vibrations of a revolving cylinder or bell’ published in the Proceedings of the Cambridge Philosophical Soci ety in 1892 [1]. In this paper he mathematically described the nature of the beats that are heard as a result of rotating a vibrating shell about its symmetric (or cylindrical axis). In a vibrating shell such as a wine glass, rotation of the wineglass about its stem will cause the nodes of vibration on the lip of the shell to move at an angular velocity (or precession rate) that is slower than the shell itself. From this observation and concept the modern HRG Inertial Instrument had its beginning. The physics of the HRG is based on the forces aris ing from Coriolis acceleration. This is the same force that drives direction of winds and ocean currents to the right and left in the northern and southern hemi spheres, respectively. The effect was first observed by GaspardGustave Coriolis, a French scientist who in 1835 described the forces that arise from the motion of an object in a rotating reference frame [2]. While concept, theory, and understanding was fully available by the late 19th century it would take another half century for the team at the Delco Wakefield
Research and Development facility in Massachusetts to rediscover the original work that G.H. Bryan had done. In 1965 a research group was formed and was headed by Dr. David Lynch, where the group’s charter was to investigate “unconventional inertial instru ments.” As a result of this early development work the modern HRG was born and found its way into practi cal applications [3]. MOTIVATION There exist a need for a small, lightweight, robust system that can be used in high accuracy navigation and precision pointing applications. Currently avail able MEMS technology have been able to take us part of the way there by providing small and lightweight solutions but are sometimes lacking in robustness and the ability to achieve navigation grade performance levels. The HRG technology with refinements can bridge the gap and provide the necessary robustness and performance levels needed. Inertial navigation technology and systems can provide a method of mak ing azimuth and elevation measurements that are independent of the earth’s magnetic field and other external/local magnetic influences. While a digital magnetic compass (DMC) response is instantaneous; its accuracy is unreliable because of its susceptibility to magnetic field influences. In order to ‘null’ the effect
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Gyro Performance Classification Class of Gyro
Bias
ARW
Rate Gyro
50°/h to 10°/h
10°/√h to 3°/√h
Tactical/Northfinding Gyro
10°/h to 0.1°/h
2°/√h to 0.05°/√h
≤0.01°/h
≤0.001°/√h
Navigation/Precision Pointing Gyro
of local magnetic field distortion the DMC must go through a time consuming local field calibration pro cess each time it is moved or a magnetic anomaly is brought near the DMC. On the other hand an all iner tial solution requires minimal field calibration and allows direct North alignment of the system in the local position via gyrocompassing. Depending on the performance level of the inertial instrument and the desired pointing accuracy the alignment time can be on the order of 60 to 120 seconds. Shown in Table is a broad categorization of gyro types and associated key performance levels in Angle Random Walk (ARW) and bias stability, this classifica tion is independent of gyro technology type. It is these two values that play an important role in the overall time to alignment and the time duration for a maintaining a specific pointing or heading accuracy. From the perspective of gyrocompassing the iner tial system can be used to resolve the horizontal (tan gential) and vertical (perpendicular) components of the Earth’s rotation vector, ΩE, ωH and ωV, respec tively. For any given latitude λ, the magnitude of these components can be computed via ω H = Ω E cos ( λ ); (1) ω V = Ω E sin ( λ ). (2) During gyro compass alignment, North is inertially determined by finding the direction of the horizontal component of the Earth’s rotation rate in the local level tangent plane. Two accelerometers are used to determine the local horizontal plane, and two local in plane orthogonal gyros are used to measure the local
ωH
N
YN ψ
E
U XN
Fig. 1. Angle rate measurement from two orthogonal gyros in the horizontal plane.
angular rate. The two orthogonal gyro axes, XN and YN, sense the horizontal component of the local earth rate. Illustrated in Fig. 1 are the two orthogonal gyro axes oriented at some angle Ψ with respect to the Earth’s rotation axis. The angle Ψ represents this true heading of the two axis system. The value of Ψ is computed using the following equation;
⎛ −ω ⎞ (3) Ψ = arctan ⎜ XN ⎟ . ⎝ ωYN ⎠ Where the values ωXN and ωYN are the horizontal angular rate components of the XN and YN gyros, respectively, and can be calculated by the following equations; (4) ωXN = −ωH sin(Ψ). (5) ωYN = ωH cos(Ψ). In the case where Ψ = 0, i.e., the gyros are aligned with North and East, the expected output from the East pointing gyro, XN, would be zero if we lived in a perfect world. Since this is not the case there is a mea surable output seen on the East gyro and it represents the bias error of the gyro and can be considered a con tamination in the output value. Therefore equation (5) can be rewritten as; ω XN = −ωH sin(Ψ) + bias. The sensitivity of the gyrocompass heading align ment to the gyro bias error is the ratio of the gyro bias error to the horizontal component of earth rate. Sim ply put, the gyrocompass alignment error is dependent on gyro bias and the latitude of the measurement as illustrated in Fig. 2. The effect of gyro bias error can be mitigated by using a two position azimuth measurement. If the sys tem is set to some arbitrary angle Ψ = α, and then rotated to Ψ = α ± 180 the instrument errors can be observed and used as a correction factor for the head ing reading. Another important aspect is the time to perform the azimuth measurement. The uncertainty of the azi muth measurement, δΨ, is dependent on the time to resolve the gyro output in the presence of noise, δω. The primary component of noise driving the measure ment uncertainty is the Angle Random Walk; there fore δω can be expressed in terms of the ARW and used to calculate the alignment time of the system.
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Heading Error versus Gyro Bias 10000
Heading Error, mils
1000
100
10
1 0 deg 45 deg 60 deg 80 deg
0.1
0.01 0.001
0.01
0.1 Bias, deg/h
1.0
10
Fig. 2. Alignment/Heading associated with gyro bias and latitude.
The uncertainty in the measurement of the heading angle, Ψ, is found to be proportional to the ARW and 1/√t where t is the time of the alignment process. Illus trated in Fig. 3 are the alignment times for three sam ple ARW values, 0.001°/√h, 0.05°/√hr and 3.5°/√h. HEMISPHERICAL RESONATOR GYRO OPERATION As noted previously the HRG shape is that of a hemispherical shell or wineglass with a rigid fixed attachment point at the base of the hemisphere. If the
Heading Error, mils
10 9 8 7 6 5 4 3 2 1 0
ARW 0.001 0.05
20
40
3.5
1500 1350 1200 1050 900 750 600 450 300 150
Standing Wave Pattern Heading Error, mils
ARW Affect on Heading Error at 45 deg Latitude
shell is struck at the upper rim, the hemisphere’s rim will be set into motion and produce a standing wave that resonates at a specific frequency. If struck cor rectly, the standing wave produced will be of the lowest order mode for a hemispheric shell and will produce a pure tone frequency. The motion of the hemisphere’s rim is in the radial direction with points of maximum deflection being defined as antinodes and the points of no radial motion defined as the nodes. Illustrated in Fig. 4 is a representation of the standing waves formed on the rim of a hemispheric shell and the associated nodes and antinodes for the lowest order frequency.
Resonator Static Position
60 80 100 120 140 160 180 200 Alignment Time, s Fig. 4. Standing wave pattern superimposed on an HRG shell.
Fig. 3. Heading error versus alignment time. GYROSCOPY AND NAVIGATION
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MEYER, ROZELLE Reference Point
Standing Wave Node
N N
N Antinode N
27° = 0.3 × 90°
N
Input Axis
N N
ωin
27° N
0.3
θout
S Transfer Function
90° Flexing Pattern Processing Angle Rotation Angle 50830
Fig. 5. Standing wave pattern rotation lag in HRG.
For illustration purposed the antinode displacement is greatly exaggerated, in reality the displacement motion is on the order of a few microns. The positions of the antinode and nodes are stable with respect to the shell, if however the shell is rotated about the anchor point or stem, the standing wave pat ter lags the physical rotation of the shell by a precise amount. The lag for a hemispherical shell is approxi mately 0.3 of the angle rotated with the 0.3 factor termed the geometric scale factor of the gyro. Simply, if the shell is physically rotated 90 deg, the standing wave pattern lags behind by 27 deg. Figure 5 illustrates the behaviour of the HRG shell when subjected to a 90 deg counterclockwise rotation. The vibration pattern is sustained via a set of elec trodes that are placed externally and circumferentially around the hemispheric shell. The electrodes act as forcers to drive the shell into motion via electrostatics. The positions and amplitudes of the antinodes and nodes are sensed via a second set of electrodes placed internally and circumferentially around the shell. These pickoff electrodes measure (sense) the displace ment of the shell via the capacitance change. Control of the standing wave pattern is accomplished by feed ing the sensed signal to a control loop that controls the forcer electrodes. Depending on the method of control desired the feedback servo for controlling the flex pattern can allow the standing wave to either precess freely with the physical rotation of the hemisphere, or cause the standing wave to maintain a fixed position during physical rotation of the hemisphere. In the former the device is said to be operating open loop or Whole Angle (WA) mode, while in the latter case the device is operating closed loop or in a Force Rebalance (FR) mode. Each has advantages of operation. For high dynamic range applications operation in the WA mode is preferred. Readout is accomplished via direct measurement of the pickoff values which indicate the
location of the standing wave with respect to a case ref erence. In this mode the geometric scale factor of the standing wave precession rate is extremely stable and has been shown to be stable to parts per billion. In FR mode, the standing wave is maintained at a position fixed relative to the case reference. This is accom plished by applying a feedback voltage to the forcer electrodes to lock the position of the standing wave. The voltage that needs to be applied is proportional to the rotation rate of the unit. This mechanization has the advantage of having better noise and bias perfor mance compared to the WAmode. However, there is a sacrifice in the limiting of rate capability. The choice of operating mode is dependent on the application that the gyro will be used in; for high rate the obvious choice is the WA while the FA would be the mode of choice for low rate precision applications. Both mechanizations have their place in the imple mentation and application space of the HRG. MHRG – NAVIGATION AND PRECISION POINTING The current embodiment of the production HRG is optimised for space applications, and therefore the units are designed to meet the challenges and require ments for space rated hardware. This unit has a case diameter of roughly 2.2 inches (5.6 cm) and weighs 0.64 pounds (290.3 grams). By comparison, the newly designed mHRG’s case diameter is 1.4 inches (3.5 cm) with a weight of only 0.25 pounds (113.4 grams). More impressive is the reduction in the major parts counts; the mHRG has 90% fewer parts than the present production version. However, when compared to the standard unit the reduction in size and parts count does not cause a significant reduction in the overall bias, ARW, or Angle White Noise (AWN) values which have been demonstrated to be 0.00035 °/h, 0.0003 °/√h, and 0.0013 arcsec/√hz,
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(b)
Fig. 6. HRG configurations, Space HRG (a) and mHRG (b).
Fig. 7. mHRG inertial measurement unit concept.
respectively. Shown in Fig. 6 are the standard space HRG and mHRG configurations. Starting with the mHRG as the core for a six (6) degree of freedom inertial measurement unit (IMU), a concept system design has been developed. The con cept design is significantly smaller than any competing design having equivalent performance levels. As designed, the unit includes the vibration isolation that can be used to isolate the IMU in high vibration appli cations. Shown in Fig. 7 is the mHRG IMU concept. The estimated size, weight and power for this unit are 23 cubic inches (377 cm3), 1.66 pounds (752 grams), and 5 watts, respectively. Maintaining a high level of performance in this size package is also important. Models have been run to get a better feel for the expected initialization time, and time to maintain a specific heading uncertainty. Initialization time has been defined earlier as the time it will take the system to achieve a specific head ing accuracy. Using a mHRG error budget of 0.001°/h, 0.0001°/√h, and 0.005 arcsec/√hz for bias, ARW, and AWN, respectively, the time to achieve a 1 milliradian error is roughly 200 seconds at 45 degrees latitude. The alignment time value also includes the GYROSCOPY AND NAVIGATION
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contribution of the accelerometer error budget. A graph of heading error versus time for the above error budget is shown in Fig. 8. Owing to the alignment pro cess that is used, once the process has started it is a completely handsoff initialization mechanization eliminating the requirement for the operator to physi cally reorient the unit to complete the alignment. Once the gyro has been aligned and operating in a free mode of operation (i.e., no external updates from GPS or other external means) the angle uncertainty will grow as the time from alignment increases. The performance quality of the gyro used will determine how fast this error increases with time. Another way to look at this is how much time is available to the user before the error in the angle measure exceeds a prede termined threshold. Once this error threshold is exceeded the user must then realign or reinitialize the IMU. Figure 9 graphically depicts the increase in angle uncertainty with time for various grades of gyro performance. Since the predicted noise and bias stability of the mHRG is in the same class as the space gyro, the mod eled performance is shown to exceed that of a naviga tion grade gyro. Therefore, from a theoretical view the
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MEYER, ROZELLE Heading Error 9 Latitude = 45 deg Azimuth Error (mils 1sigma)
8 2.5mil PE(50%) at 60 s 1.4mil PE(50%) at 80 s
7 6 5
1mil PE(50%) at 105 s
4 3 2 1
1mil PE(50%) 1mil 1sigma
0
50
100
150 Time, sec
200
250
300
F Fig. 8. mHRG initialization performance simulation.
PERFORMANCE CHART ANGLE (Orange Chart) ANGLE Uncertainty Vs Time (Orange Chart) Shows Time Alignment Can be Maintained Rate Gyro
Tactical Gyro Nav Gyro
Space Gyro
10–1
100
101
102 tau, sec
103
104
105
Fig. 9. Angle uncertainty as a function of time.
size and performance of a mHRG based IMU makes it an interesting candidate for navigation and precision pointing applications.
In order to reduce the size and complexity of the mHRG, elements from the space gyro had to be elim inated creating a concern that performance would be
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MILLIHRG INERTIAL NAVIGATION SYSTEM Compensated North input Error (1), Temperature (2), Bias Estimate (3)
60
1
0 Rate Estimate Error Temperature Bias Estimate
–0.1 –0.2
40
2 20
–0.3 3
–0.4 –0.5 0
5
10
15 20 25 Time, h
30
35
Temperature, °C Output Error, degree/h
Drift Error, degree/h
0.1
0 40
233
Compensated North input Error, Average error 300 second sum
0.01 0.08 0.06 0.04 0.02 0 –0.02 –0.04 –0.06 –0.08 –0.01
Rate Estimate Error
Mean: 0.0003°/h Std Dev: 0.004°/h 0
5
10
15 20 Time, h
25
30
35
40
1sigma Rate Uncertainties, °/h
Fig. 10. Rate estimate error of temperature.
AUTOFIT (sqrt allen variance of rate)
102
mHRG Demonstration Test Data 8s to resolve 0.01°/h Drift Test Data
101 100
10–1
Noise Test Data
0.01°/h
10–2
0.001°/hr
10–3 10–4 10–3
Cal Drift Test Data
60 s 10–2
10–1
101 tau, s
100
102
103
104
105
Fig. 11. mHRG demonstration test using selfcalibration.
degraded. In order to maintain an equivalent level of performance a selfcalibration methodology has been implemented. This method has been shown to be effective in long term laboratory testing at ambient temperatures as well as during dynamic thermal cycling conditions. Measurements made at laboratory ambient for bias stability and ARW show performance levels at 0.0005°/h and 0.00015°/√h, respectively. Applying selfcalibration to dynamic thermal testing showed extremely positive results and demonstrated the removal of temperature induced bias errors with out the need for prior instrument calibration. Earth rate measurement accuracy was to an accuracy of 0.0003°/h over a temperature range of +5 to +50°C (the temperature range in these tests was limited by the thermal range of the breadboard electronics not the GYROSCOPY AND NAVIGATION
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gyro). Shown in Fig. 10 is the rate estimate error ther mal performance of the gyro. The data shows a bias error reduction of three orders of magnitude com pared to the nonselfcalibration data. Additional noise, drift, and calibration drift testing was performed. A composite of this data is plotted and shown in Fig. 11. The data clearly shows the capabili ties of the mHRG which, after 8 seconds of operation the gyro, was at a rate uncertainty level of 0.01°/h. At 60 seconds of operation the rate uncertainty approaches 0.001°/h and continues to decline with increasing time. When comparing this data to the rate uncertainty of a navigation grade and space gyro, the mHRG surpasses navigation grade performance a roughly 8 seconds and continues to trend downward with time. Normally the rate uncertainty plot shows an
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initial down trend with time and then a levelling out to a constant minimum value. The mHRG data thus far taken does not show this typical behaviour and can be seen in Fig. 11. The behaviour is attributed to the implementation of selfcalibration.
implementation of a selfcalibration mechanization. With the speed in which it reaches a prescribed rate uncertainty/alignment, the ability to hold attitude performance over extended time durations, and its reduced physical size makes the mHRG a promising technology for terrestrial applications.
CONCLUSIONS In this paper we have discussed HRG technology and the path leading to the development of a mHRG which has been accomplished without the sacrifice in basic performance of the gyro. Performance was dem onstrated in the laboratory environment dynamically over a temperature range from +5 to +50 °C. Test results show that a precision inertial navigation system with low bias stability (0.00035°/hr) and ARW (0.0003°/√hr) are possible with the mHRG and the
REFERENCES 1. Bryan, G.H., On the Beats in the Vibrations of a Revolving Cylinder or Bell, Proceedings of the Cam bridge Philosophical Society, 1892, vol VII. 2. Coriolis, G.G., Mémoire sur les équations du movement relative des systèms de corps (On the Equation of Rela tive Motion of a Systems of Bodies), J. Ec. Polytech, 1835, no. 15, pp. 142154. 3. Rozelle, D.M., The Hemispherical Resonator Gyro: from Wineglass to the Planets, AAS 2009.
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